Show that the points `A(-2 hati+3 hatj+5 hatk)`, `B(hati+2 hatj+3 hatk)` and `C(7 hati-hatk)` are collinear.

Show that the points with position vectors '2 hati+6 hatj+3 hatk, hati+2 hatj+7 hatk' and '3 hati+10 hatj-hatk' are collinear.

Show that the points with position vectors 2hati+6hatj+3hatk,hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

Show that the vectors 2 hati-hatj+hatk, hati-3 hatj-5 hatk and 3 hati-4 hatj-4 hatk form the vertices of a right-angled triangle.

Show that the vectors 2 hati-3 hatj+4 hatk and -4 hati + 6 hatj-8 hatk are collinear.

Given the position vectors of three points A(hati-hatj+2hatk ),B(4hati+5hatj+8hatk) and C(3hati+3hatj+6hatk) . Find the projection of vec(AB) on vec(AC) .

Given the position vectors of three points A(hati-hatj+2hatk ),B(4hati+5hatj+8hatk) and C(3hati+3hatj+6hatk) . Prove that A,B and C are collinear.

If the vectors 2hati + 2hatj + 6hatk, 2hati + 6hatj + 2hatk+ lambdahatj+6hatk and 2hati - 3hatj + hatk are coplanar, then the value of lambda is

Find the angle between the following pairs of lines: i) vecr=2 hati-5 hatj+hatk+lambda(3 hati+2 hatj+6 hatk) and vecr=7 hati-6 hatk+mu(hati+2 hatj+2 hatk) (ii) vecr=3 hati+hatj-2 hatk+lambda(hati-hatj-2 hatk) and vecr=2 hati-hatj-5 6 hatk+mu(3 hati-5 hatj-4 hatk)

If hati+hatj+hatk, 2 hati+5 hatj, 3 hati+2 hatj-3 hatk and hati-6 hatj-hatk are the position vectors of points A, B , C and D respectively, then find the angle between bar(AB) and bar(CD) . Deduce that bar(AB) and bar(CD) are collinear.